The familiarity of the Brandenburgs should not blind us to their magnitude. I’m convinced that Bach is the greatest genius who ever walked among us, and the Brandenburgs are what he wrote when he was happy.

A piece of music will draw one in, teach one about its structure and secrets, whether one is listening consciously or not. This is so even if one has never heard a piece of music before. Listening to music is not a passive process but intensely active, involving a stream of inferences, hypotheses, expectations, and anticipations (as David Huron and others have explored). We can grasp a new piece – how it is constructed, where it is going, what will come next – with such accuracy that even after a few bars we may be able to hum or sing along with it.

Another difficulty was mentioned to me by the neurologist and musician Steven Frucht, who himself has absolute pitch. He sometimes experiences a certain difficulty in hearing intervals or harmonies because he is so conscious of the chroma of the notes that compose them. If, for example, one plays a C on the piano and the F-sharp above this, he might be so conscious of the C-ness of the C and the F-sharpness of the F-sharp that he fails to notice that they form a tritone, a dissonance which makes most people wince.

Although a teaspoon of Mozart may not make a child a better mathematician, there is little doubt that regular exposure to music, and especially active participation in music, may stimulate development of many different areas of the brain – areas which have to work together to listen to or perform music. For the vast majority of students, music can be every bit as important educationally as reading or writing.

It really is a very odd business that all of us, to varying degrees, have music in our heads. If Arthur C. Clarke’s Overlords were puzzled when they landed on Earth and observed how much energy our species puts into making and listening to music, they would have been stupefied when they realized that, even in the absence of external sources, most of us are incessantly playing music in our heads.

But why this incessant search for meaning or interpretation? […] Music can have wonderful, formal, quasi-mathematical perfection, and it can have heartbreaking tenderness, poignancy, and beauty (Bach, of course, was a master at combining these). But it does not have to have any “meaning” whatever. One may recall music, give it the life of imagination (or even hallucination) simply because one likes it – this is reason enough.